Chapter 2 Quadratics - Year 1

Question 1

What so you do when you find a hidden quadratic?

Answer 1

You write it in terms of another letter.
You say that a letter is = to the x term with no power
You then solve the quadratic with your term
Then you substitute the x term back into the equation and solve for x

Question 2

Answer 2

You should substitute your value back in to see if it is a real value or not

Question 3

Answer 3

Question 4

What is the domain of a function?

Answer 4

The set of possible inputs of a function

Question 5

What is the range of a function?

Answer 5

The set of possible outputs of the function

Question 6

How do you right x is a member of all real numbers?

Answer 6

Question 7

What does this mean?

Answer 7

That x is a member of all real numbers

Question 8

What are the roots of an equation?

What are some other words for roots?

Answer 8

When f(x) = 0 (where the graph crosses the x axis)

The roots/zeros/solutions

Question 9

What do you do when a question asks you to find all the values for which f(x)=g(x)

Answer 9

You put them equal to each other and solve

Question 10

What do you do when a question asks you to find the roots of a function?

Answer 10

Put the function equal to 0
Solve the equation of the function

Question 11

What do you do when a question asks you to determine the minimum value of a function?

Answer 11

You find the minimum value through completing the square or differentiation.
THE MINIMUM VALUE WILL BE THE Y VALUE
You then state that the minimum value is y and it occurs when x = …

Question 12

What does sketch mean?
How do you do this if you are given a normal quadratic?
What values do you include?

Answer 12

You draw a rough diagram of it. It is not meant to be accurate.

You solve the equation to find the roots - this is where the graph will cross the x axis
If the x^2 is negative then it will be a sad quadratic

You should include the roots, turning point, where it crosses every axis.
Normally the question will tell you what it wants

Question 13

How so you deduce the equation of a quadratic if you are given a sketch?

Answer 13

You are normally given the roots so you know the answers to the equation
You then reverse the sign on each root and write it in the for (x+a)(x+b)
You then expand the brackets.
You may be given y intercept
You know that the value without an x in your equation will be the y intercept so you need to work out what you need to multiply your equation by so that the y intercept match
Make sure to check if the quadratic is sad or happy so you know if you need to multiply for -1 or not

Question 14

What is the discriminant?

Answer 14

Question 15

If a quadratic has 2 roots what do we know about the discriminant?

Answer 15

b^2-4ac > 0
The discriminant is positive

Question 16

If a quadratic has 1 roots what do we know about the discriminant?

Answer 16

b^2-4ac = 0
The discriminant is equal to 0

Question 17

If a quadratic has no roots what do we know about the discriminant?

Answer 17

b^2-4ac < 0
The discriminant is negative

Question 18

What phrase should make you think discriminant?

Answer 18

Equal roots
The discriminant will be 0

Question 19

What should you do if you are given a quadratic equation with unknowns in it and told that it has either 2 roots, equal roots or no roots?

Answer 19

Right out the discriminant and state that it is equal to 0 (b^2-4ac = 0)
Then write a=, b= and c= down your page
You should wrote the corresponding values next to a,b and c (ax^2+bx+c)
Then substitute your values into your equation of b^2-4ac = 0
Solve the equation for the answer

Question 20

What is the answer to a 1 mark question “what does the constant mean in this equation” in a quadratic?

Answer 20

The height of something (a tower)

Question 21

How do you calculate how long an object was in the air for?

Answer 21

Put the equation =0
Solve the equation
Do either t-0 (if 1 value of t is negative)
Or
T2-T1

Question 22

How do you find the maximum height of an object above the ground if it is modelled as a quadratic

Answer 22

Complete the square or differentiate
You can then find the turning point

A height of x at y seconds

Question 23

When do you use U or N when using set notation?

Answer 23

If it is <0 it will always be 1 continues module

When it is >0 you will always have to use the or (u) sign with 2 different modules

Question 24

Factorise this?
What can’t you do?
Why?

Answer 24

You can’t divide because you will loose a solution

Question 25

How many solutions does x^5-5 have?

How do you know this?

Answer 25

1 real solution

The graoh of x^5 would only habe 1 real solution at the origin.
With the -5 you are just translating the graph 5 units to the right so there will only be 1 real solution